#pragma GCC optimize(3, "unroll-loops", "no-stack-protector")
#define atsum(l, r) accumulate(l, r, 0)
#include <bits/stdc++.h>

#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/hash_policy.hpp>
using namespace std;
using ll = long long;
using ull = unsigned long long;
constexpr int inf = 0x3f3f3f3f;
constexpr ll INF = 0x3f3f3f3f3f3f3f3f;
template <typename T>
inline void chkmin(T &x, T y) {
    x = min(x, y);
}
template <typename T>
inline void chkmax(T &x, T y) {
    x = max(x, y);
}
namespace FastIO {
// ------------------------------
#define IN_HAS_NEG
#define OUT_HAS_NEG
#define CHK_EOF
#define DISABLE_MMAP
// ------------------------------
#if __cplusplus < 201400
#error Please use C++14 or higher.
#endif
#if __cplusplus > 201700
#define INLINE_V inline
#else
#define INLINE_V
#endif
#if (defined(LOCAL) || defined(_WIN32)) && !defined(DISABLE_MMAP)
#define DISABLE_MMAP
#endif
#ifndef DISABLE_MMAP
#include <sys/mman.h>
#endif
#ifdef LOCAL
inline char gc() { return getchar(); }
inline void pc(char c) { putchar(c); }
#else
#ifdef DISABLE_MMAP
INLINE_V constexpr int _READ_SIZE = 1 << 18;
INLINE_V static char _read_buffer[_READ_SIZE], *_read_ptr = nullptr,
                                               *_read_ptr_end = nullptr;
inline char gc() {
    if (__builtin_expect(_read_ptr == _read_ptr_end, false)) {
        _read_ptr = _read_buffer;
        _read_ptr_end =
            _read_buffer + fread(_read_buffer, 1, _READ_SIZE, stdin);
#ifdef CHK_EOF
        if (__builtin_expect(_read_ptr == _read_ptr_end, false)) return EOF;
#endif
    }
    return *_read_ptr++;
}
#else
INLINE_V static const char *_read_ptr =
    (const char *)mmap(nullptr, INT_MAX, 1, 2, 0, 0);
inline char gc() { return *_read_ptr++; }
#endif
INLINE_V constexpr int _WRITE_SIZE = 1 << 18;
INLINE_V static char _write_buffer[_WRITE_SIZE], *_write_ptr = _write_buffer;
inline void pc(char c) {
    *_write_ptr++ = c;
    if (__builtin_expect(_write_buffer + _WRITE_SIZE == _write_ptr, false)) {
        fwrite(_write_buffer, 1, _write_ptr - _write_buffer, stdout);
        _write_ptr = _write_buffer;
    }
}
INLINE_V struct _auto_flush {
    ~_auto_flush() {
        fwrite(_write_buffer, 1, _write_ptr - _write_buffer, stdout);
    }
} _auto_flush;
#endif
#ifdef CHK_EOF
inline bool _isdigit(char c) { return (c & 16) && c != EOF; }
inline bool _isgraph(char c) { return c > 32 && c != EOF; }
#else
inline bool _isdigit(char c) { return c & 16; }
inline bool _isgraph(char c) { return c > 32; }
#endif
template <class T>
INLINE_V constexpr bool _is_integer = numeric_limits<T>::is_integer;
template <class T>
INLINE_V constexpr bool _is_signed = numeric_limits<T>::is_signed;
template <class T>
INLINE_V constexpr bool _is_unsigned = _is_integer<T> && !_is_signed<T>;
template <>
INLINE_V constexpr bool _is_integer<__int128> = true;
template <>
INLINE_V constexpr bool _is_integer<__uint128_t> = true;
template <>
INLINE_V constexpr bool _is_signed<__int128> = true;
template <>
INLINE_V constexpr bool _is_unsigned<__uint128_t> = true;
#undef INLINE_V
inline void read(char &c) {
    do c = gc();
    while (!_isgraph(c));
}
inline void read_cstr(char *s) {
    char c = gc();
    while (!_isgraph(c)) c = gc();
    while (_isgraph(c)) *s++ = c, c = gc();
    *s = 0;
}
inline void read(string &s) {
    char c = gc();
    s.clear();
    while (!_isgraph(c)) c = gc();
    while (_isgraph(c)) s.push_back(c), c = gc();
}
#ifdef IN_HAS_NEG
template <class T, enable_if_t<_is_signed<T>, int> = 0>
inline void read(T &x) {
    char c = gc();
    bool f = true;
    x = 0;
    while (!_isdigit(c)) {
        if (c == 45) f = false;
        c = gc();
    }
    if (f)
        while (_isdigit(c)) x = x * 10 + (c & 15), c = gc();
    else
        while (_isdigit(c)) x = x * 10 - (c & 15), c = gc();
}
template <class T, enable_if_t<_is_unsigned<T>, int> = 0>
#else
template <class T, enable_if_t<_is_integer<T>, int> = 0>
#endif
inline void read(T &x) {
    char c = gc();
    while (!_isdigit(c)) c = gc();
    x = 0;
    while (_isdigit(c)) x = x * 10 + (c & 15), c = gc();
}
inline void write(char c) { pc(c); }
inline void write_cstr(const char *s) {
    while (*s) pc(*s++);
}
inline void write(const string &s) {
    for (char c : s) pc(c);
}
#ifdef OUT_HAS_NEG
template <class T, enable_if_t<_is_signed<T>, int> = 0>
inline void write(T x) {
    char buffer[numeric_limits<T>::digits10 + 1];
    int digits = 0;
    if (x >= 0) do
            buffer[digits++] = (x % 10) | 48, x /= 10;
        while (x);
    else {
        pc(45);
        do buffer[digits++] = -(x % 10) | 48, x /= 10;
        while (x);
    }
    while (digits) pc(buffer[--digits]);
}
template <class T, enable_if_t<_is_unsigned<T>, int> = 0>
#else
template <class T, enable_if_t<_is_integer<T>, int> = 0>
#endif
inline void write(T x) {
    char buffer[numeric_limits<T>::digits10 + 1];
    int digits = 0;
    do buffer[digits++] = (x % 10) | 48, x /= 10;
    while (x);
    while (digits) pc(buffer[--digits]);
}
template <int N>
struct _tuple_io_helper {
    template <class... T>
    static inline void _read(tuple<T...> &x) {
        _tuple_io_helper<N - 1>::_read(x), read(get<N - 1>(x));
    }
    template <class... T>
    static inline void _write(const tuple<T...> &x) {
        _tuple_io_helper<N - 1>::_write(x), pc(32), write(get<N - 1>(x));
    }
};
template <>
struct _tuple_io_helper<1> {
    template <class... T>
    static inline void _read(tuple<T...> &x) {
        read(get<0>(x));
    }
    template <class... T>
    static inline void _write(const tuple<T...> &x) {
        write(get<0>(x));
    }
};
template <class... T>
inline void read(tuple<T...> &x) {
    _tuple_io_helper<sizeof...(T)>::_read(x);
}
template <class... T>
inline void write(const tuple<T...> &x) {
    _tuple_io_helper<sizeof...(T)>::_write(x);
}
template <class T1, class T2>
inline void read(pair<T1, T2> &x) {
    read(x.first), read(x.second);
}
template <class T1, class T2>
inline void write(const pair<T1, T2> &x) {
    write(x.first), pc(32), write(x.second);
}
template <class T1, class... T2>
inline void read(T1 &x, T2 &...y) {
    read(x), read(y...);
}
template <class... T>
inline void read_cstr(char *x, T *...y) {
    read_cstr(x), read_cstr(y...);
}
template <class T1, class... T2>
inline void write(const T1 &x, const T2 &...y) {
    write(x), write(y...);
}
template <class... T>
inline void write_cstr(const char *x, const T *...y) {
    write_cstr(x), write_cstr(y...);
}
template <class T>
inline void print(const T &x) {
    write(x);
}
inline void print_cstr(const char *x) { write_cstr(x); }
template <class T1, class... T2>
inline void print(const T1 &x, const T2 &...y) {
    print(x), pc(32), print(y...);
}
template <class... T>
inline void print_cstr(const char *x, const T *...y) {
    print_cstr(x), pc(32), print_cstr(y...);
}
inline void println() { pc(10); }
inline void println_cstr() { pc(10); }
template <class... T>
inline void println(const T &...x) {
    print(x...), pc(10);
}
template <class... T>
inline void println_cstr(const T *...x) {
    print_cstr(x...), pc(10);
}
}  // namespace FastIO
using namespace FastIO;
template <typename T>
inline void clear(T &x) {
    T y;
    swap(x, y);
}
template <uint32_t mod = 998244353>
class Modint {
   private:
    static constexpr uint32_t get_r() {
        uint32_t ret = mod;
        for (int i = 0; i < 4; i++) ret *= 2 - mod * ret;
        return ret;
    }
    static constexpr uint32_t r = get_r();
    static constexpr uint32_t n2 = -uint64_t(mod) % mod;
    static_assert(r * mod == 1 && mod < (1 << 30) && mod & 1);
    uint32_t data;

   public:
    constexpr Modint() : data(0) {}
    template <class int_t>
    constexpr Modint(const int_t x)
        : data(reduce(
              uint64_t((sizeof(int_t) < sizeof(uint32_t) ? x : x % int_t(mod)) +
                       mod) *
              n2)){};
    static constexpr uint32_t reduce(const uint64_t x) {
        return (x + uint64_t(uint32_t(x) * (-r)) * mod) >> 32;
    }
    constexpr Modint &operator+=(const Modint &r) {
        if (int32_t(data += r.data - 2 * mod) < 0) {
            data += 2 * mod;
        }
        return *this;
    }
    constexpr Modint &operator-=(const Modint &r) {
        if (int32_t(data -= r.data) < 0) {
            data += 2 * mod;
        }
        return *this;
    }
    constexpr Modint &operator*=(const Modint &r) {
        return data = reduce((uint64_t)data * r.data), *this;
    }
    constexpr Modint &operator/=(const Modint &r) { return *this *= r.inv(); }
    constexpr friend Modint operator+(Modint l, const Modint &r) {
        return l += r;
    }
    constexpr friend Modint operator-(Modint l, const Modint &r) {
        return l -= r;
    }
    constexpr friend Modint operator*(Modint l, const Modint &r) {
        return l *= r;
    }
    constexpr friend Modint operator/(Modint l, const Modint &r) {
        return l /= r;
    }
    constexpr friend bool operator==(Modint l, const Modint &r) {
        return l.value() == r.value();
    }
    constexpr Modint operator-() const { return Modint() - Modint(*this); }
    template <class int_t>
    constexpr Modint pow(int_t r) const {
        Modint res(1), w(*this);
        for (; r; r >>= 1, w *= w)
            if (r & 1) res *= w;
        return res;
    }
    constexpr Modint inv() const { return pow(mod - 2); }
    constexpr uint32_t value() const {
        uint32_t res = reduce(data);
        return res >= mod ? res - mod : res;
    }
};
using modint = Modint<>;

namespace cmaths {
const int FACMAX = 1e7 + 10;
modint fac[FACMAX], ifac[FACMAX], inv[FACMAX];
inline void initfac(int n) {
    fac[0] = 1;
    for (int i = 1; i <= n; i++) fac[i] = fac[i - 1] * i;
}
inline void initifac(int n) {
    ifac[n] = fac[n].inv();
    for (int i = n - 1; ~i; i--) ifac[i] = ifac[i + 1] * (i + 1); 
}
inline modint C(int a, int b) { return a < b ? 0 : fac[a] * ifac[b] * ifac[a - b]; }
inline modint A(int a, int b) { return a < b ? 0 : fac[a] * ifac[a - b]; }
inline void getInv(int k) {
    inv[1] = 1;
    for (int i = 2; i <= k; ++i) inv[i] = ifac[i] * fac[i - 1];
}
inline void initall(int n = FACMAX - 2) { initfac(n), initifac(n), getInv(n); }
};
using namespace cmaths;

const int N = 2e5 + 10;
int cid, T, n, m, x[N], y[N], cnt, res, ewe;
pair<int, int> qwq[N];
const int M = 10;
basic_string<int> vec[N];
int g[M][M], dis[N], fr[N];
queue<int> q;
inline void calc(int S) {
    memset(dis, -1, sizeof(dis[0]) * (n + 2));
    dis[S] = 0, fr[S] = 0;
    q.push(S);
    while (q.size()) {
        int u = q.front();
        q.pop();
        for (int v : vec[u])
            if (dis[v] == -1) dis[v] = dis[u ] + 1, fr[v] = (u == S ? v : fr[u]), q.push(v);
    }
    for (int i = 1; i <= m; i++) {
        int u1 = x[i], v1 = y[i];
        if (dis[u1] != -1 && dis[v1] != -1 && fr[u1] != fr[v1] && (dis[u1] + dis[v1] != 1)) {
            if (res > dis[u1] + dis[v1] + 1) res = dis[u1] + dis[v1] + 1, ewe = 1;
            else if (res == dis[u1] + dis[v1] + 1) ++ewe;
        }
    }
}
inline void work() {
    ewe = 0;
    cnt = 0;
    read(n, m);
    for (int i = 1; i <= n; i++) clear(vec[i]);
    for (int i = 1; i <= m; i++) read(x[i], y[i]), vec[x[i]] += y[i], vec[y[i]] += x[i];
    if (n <= 5) {
        for (int u = 1; u <= n; u++)
            for (int v = u + 1; v <= n; v++) qwq[cnt++] = make_pair(u, v);
        ll ans = inf, ansc = 0;
        for (int i = 0; i < (1 << cnt); i++)
            if (__builtin_popcount(i) == m - 1) {
                memset(g, 0x3f, sizeof(g));
                for (int j = 1; j <= n; j++) g[j][j] = 0;
                for (int j = 0; j < cnt; j++)
                    if (i >> j & 1)
                        g[qwq[j].first][qwq[j].second] =
                            g[qwq[j].second][qwq[j].first] = 1;
                for (int k = 1; k <= n; k++)
                    for (int i = 1; i <= n; i++)
                        for (int j = 1; j <= n; j++)
                            chkmin(g[i][j], g[i][k] + g[k][j]);
                ll sum = 0;
                for (int i = 1; i <= m; i++) sum += g[x[i]][y[i]];
                if (sum < ans)
                    ans = sum, ansc = 1;
                else if (sum == ans)
                    ++ansc;
            }
        println(-ans, ansc);
    } else {
        res = inf;
        for (int i = 1; i <= n; i++) if (vec[i].size()) calc(i);
        // --n;
        // cerr << "find youmoewe:" << ewe / res << endl;
        println(-res - m + 2, (C(3 * (res - 1), (res - 1)) * modint(2 * (res - 1) + 1).inv() * modint(ewe / res)).value());
    }
}
int main() {
    initall();
    freopen("oi.in", "r", stdin);
    freopen("oi.out", "w", stdout);
    read(cid, T);
    while (T--) work();
    return 0;
}
/*
7 5
3 3
1 2
2 3
3 1
4 4
1 2
2 3
3 4
4 1
5 5
1 2
2 3
3 4
4 5
5 1
6 6
1 2
2 3
3 4
4 5
5 6
6 1
7 7
1 2
2 3
3 4
4 5
5 6
6 7
7 1
*/
